If \(\mbox{CI-dim}\,_R(M)=0\)  then \(\mbox{CI-dim}\,_R(M^*)=0\)  by [1]} and so from the exact sequence (REF ), \(\mbox{CI-dim}\,_R(\mbox{Tr}\,M)<\infty \) .
As \(\mbox{G-dim}\,_R(M)=0\) , \(\mbox{G-dim}\,_R(\mbox{Tr}\,M)=0\)  by [2]} and so \(\mbox{CI-dim}\,_R(\mbox{Tr}\,M)=0\)  by [3]}.
As \(\underline{M}\cong \underline{\mbox{Tr}\,\mbox{Tr}\,M}\) , the other side is obvious.
